Based on the assumption that fumbles per play follow a normal distribution, you'd expect to see, according to random fluctuation, the results that the Patriots have gotten over this period, once in 16,233.77 instances

I bet if he did an analysis of point differential the best teams would be way above where they would statistically be due to random chance, so they were probably all cheaters and their super bowl wins should be vacated. Apparently doing things that help you win games makes you more likely to win!

Also the absolute number of fumbles is not an enormous outlier. Sifu is right, lying with stats to make an outlier that can be explained by skill chance whatever appear to be so shocking it must be teh ballz.
PS I am a Giants fan.

It's the same kind of shit they do in broadcasts all the time; "Tony Romo is only the third quarterback to have thrown three picks in a quarter in games played outdoors in under 55 degree weather in the past year and a month!"

I missed the update before. So now the patriots aren't even top in fumbles per game, only top among outdoor teams. WHAT ARE THE CHANCES!!!! I like how he keeps saying this can't be explained by random fluctuation. I guess playing in the NFL is like playing the slots, why do people even care about strategy or draft picks?

The link in the OP is the first thing I've read anywhere that suggests that the Patriots might have been playing with deliberately underinflated balls, not only in the playoff game against the Colts, or possibly maybe also in the playoff game against the Ravens (there have been whispers), but in all games played over the last eight years. (At least I think that is the conclusion he seems to be pointing to with his analysis.)

If there's anything at all to that, it goes from something of a joke to a legitimate scandal. And it makes doubly-silly all of the (already silly) comments about how the Patriots would have beaten the Colts with any balls so who cares if they were underinflated.

Depends on your definition of very unusual. But if you take whatever team had the best record over a given period you'll find that on some metric they're way better than you'd expect by chance. Especially when you start slicing it by smaller time periods, indoor vs outdoor, etc.

Following on 33, I guess there's no reason to think they have been using underinflated balls in every game for eight years. Probably just in games that are expected to be played in bad, wet weather (like e.g. the Colts game), where the risk of fumbles is especially significant.

The patriot defenders in this thread need to adjust their Bayesian priors. We aren't looking at the fumble statistics and trying to figure out whether they show convincing evidence that the patriots may be deflating footballs. We KNOW the Patriots have been intentionally deflating footballs. At least once, against the Colts. It seems unlikely that this was the first game in which they've pulled that trick. The fumble statistics are helping us get a sense of how long they've been pulling this trick.

Those who think the statistics are just noise reflecting the fact that the pats are a very good team across the board--why did they suddenly start getting so much better on this particular metric in 2007? Their teams were also very good before that.

Yes if we had seen this three weeks ago it wouldn't give us any special reason to think the Pats cheated, but like urple says *given that we know they cheated at least once* it's quite good evidence they've cheated a similar way in the past.

That article isn't helpful. It's legal to scuff the ball, as long as the ref approves the ball before the game. It's not legal to underinflate the ball. (It sounds like the refs really (wait for it) dropped the ball here, too.)

Eli Manning, a man who twice beat the Patriots in Super Bowls and performs almost without discernible emotion in Toyota ads, has his balls "rubbed vigorously for 45 minutes with a dark brush," scoured with a wet towel and spun on an electric wheel, the New York Times revealed in a 2013 story.

No we don't. We know some footballs were found to be lower PSI than called for, but we don't know how they got that way or who did it or if it was done intentionally or with intent to go below the 12.5 PSI lower bound.

There's also the unrelated (to Ballghazi) question of whether the rule actually has a useful purpose. Teams apparently provide their own balls. Why shouldn't they be allowed to have them at any PSI they choose? (That's Pierce's point, for those who didn't follow the link.) The NFL fine for them being outside the range is less than for "adjusting your crotch."

Moby I don't think you're reading that 25 year bit correctly. They looked at every 5yr stretch by every team over 25 years. The late model Pats are super good in that set. Not sure about the earlier model Pats.

The fumble statistics are helping us get a sense of how long they've been pulling this trick.
When the "scandal" initially broke, it was all about how Brady liked a certain feel to his balls, how soft balls were easier to throw and catch. Now suddenly it's changed to fumbles that are the proof. Again, I don't care about the Patriots, but this ex post reasoning and searching for statistical significance in some filtered stats then rationalizing for why your cause of choice explains said stat is exactly the kind of shit that gets (or should get) people canned from science jobs.
You could argue that almost any offensive stat (aside from kicking, separate balls) and possibly some defensive ones too if they have an offensive component (e.g. turnover +/-) could be related to inflation of the balls. That a team that's won their conference more often than not over the past decade ends up as an outlier in some stat does not prove that a) they consistently underinflated balls or b) even if they did that the chosen stat is related.

You don't see this kind of inverse calculation often. Batting average isn't measured in at-bats per hit, field goal percentage isn't measured in shots per make, etc.

The one case where you do see this backward statistic is miles per gallon (should be gallons per mile!) and it causes big problems there in that it makes real gas guzzlers not look so bad. The difference between a 10mpg car and a 20mpg car is not the same as 20mpg and 30mpg, instead it's the same going from a 20mpg car to one that magically runs on fairy dust. (A 10mpg vehicle takes 10 gallons to go 100 miles, a 20mpg vehicle takes 5 gallons to go 100 miles, so you'd need to use 0 gallons to go 100 miles to get the same improvement.)

One reason one might not like fumbles/play in an article is that the numbers are small and hard to get a handle on. But the solution to that is to measure things per 100 or 1000 plays (which you see all the time in Basketball stats (per 100 possessions) or medical stats (per 1000 people))..

I just ran the numbers using fumbles per 1000 plays just for last year's data. The Patriots still look like an outlier, but it's not as extreme. It's hard to tell from one year's data whether this is really normally distributed, but the Patriots (at 5.34 fumbles per 1000 plays) are 2.6 standard deviations away from the mean (9.76 fumbles per 1000 plays), while the most fumble prone team is 2 standard deviations away from the mean (13.16 fumbles per 1000 plays). That's still surprising, but naively you'd expect that something like that by chance one in every 200 times.

The main problem with the way the data is presented in the article is that it magnifies outliers on one side of the data and shrinks them on the other. So it's not just that the Patriots look like more of an outlier, the fumble-prone outliers have entirely gone away. Philly fumbles a lot!

Not really convinced. You would have to examine every NFL stat and see what kind of variance you get on every one to judge how unusual it is that a team is so way ahead of the others in a particular area (my guess is that NFL teams employ guys to do exactly that and it would have been noticed if it were that improbable).
It's not that rare to see extreme outliers, and no, the finding of the underinflated balls doesn't really says much about the statistical issue. Lots of referees saw their balls after games all these years and found them allright. And we have no idea how much of a difference it makes, anyway.

Damn it, fa, I was just about to make almost exactly that comment before refreshing the page. Which makes me wonder if it occurred to anyone to doctor a gauge just to put the whole ridiculous thing to rest.

57 et seq. Fair enough. I agree that whoever shat out the bizarre 1:16000 chance or whatever should be mocked. But I'm mystified why all the condemnation of looking at plays per fumble or its reciprocal--either makes sense to me. The analysis, such as it is, *is* incomplete--but the first step is always incomplete, so why condemn it so vociferously?

In order to evaluate whether an outlier is the kind of thing you'd expect to see by chance or an actual anomaly, you need to have some idea of what distribution you'd expect the data to have. It's somewhat plausible that fumbles/play follows something close to a normal distribution, which means you can start doing things like counting standard distributions and get some idea of whether it's a crazy outlier or an expected outlier. (It can't literally be a normal curve because there's going to be a cutoff point at 0 that you can't go below, but it could be close enough for government work.) By contrast, plays/fumble is just not the kind of variable that could be anywhere close to a normal distribution. So easy Stats 101 is totally useless and you have no idea whether the outlier is surprising or not.

There could very well still be something going on here, and it'd be great to see someone who has some clue of how statistics work (which to be clear wouldn't really include me) write an article about this data. But this article is just sloppy.

Here's one way to think about it: that first graph was "fumbles lost per play over a five year window". It's pretty well known in the football stats world that fumble recovery percentage is random (e.g. see here, scroll down). It therefore follows that if you looked at "fumbles recovered per play over a five year window" you should see the same pattern, right? Yet, in the dude's update, when he looks at "all fumbles per play over a five year window", the patriots are no longer an outlier. That means that if you look at "fumbles recovered per play over a five year window" -- which, remember, our prior knowledge about fumble recovery tells us should be basically the same -- not only are the pats not an outlier, they're somewhere well in the middle of the pack. Otherwise, the mean of "fumbles lost per play over a five year window" and "fumbles recovered per play over a five year window" (which is what "all fumbles per play over a five year window" is) would not be so much lower than "fumbles lost per play over a five year window". Why should this be? There are lots of other reasons not to trust that analysis (why a five year window? Why completely exclude teams that play their home games indoors when all teams play some games indoors and some outdoors? Why not just look at bad weather games? Why set the graph axes like that? What about statistical signficance? Why assume normality? Why do you need a "data scientist" to make up some bullshit odds for you?) but that's I think a relatively clear one.

A ref handles the ball before every play and over the course of a game will handle the other sides balls and the kicking balls repeatedly. An opponent handles the ball on every interception and fumble. Every bounce of every missed pass is filmed.

I'm not ready to believe in a years long conspiracy of underinflation.

I am willing to believe that a small number of elite athletes could develop ball handling skills that would show up in fumble stats.

73: I assume that the "fumbles" he is using in the second, updated part of the post refers to "fumbles by the team running plays" because otherwise "offensive plays by team X per fumble" makes no sense; what do fumbles when the defense (and other team's offense, and other team's footballs) is on the field have to do with anything?

74: Yeah. but it's count data with a floor in the several dozens. Not a lot of worries there.

Sifu, thanks for the response. There are totally 8 days in this week, so... I read the OPs link before the update--I totally thought it was ALL fumbles. So, certainly that clears a lot of the interestingness right out of the Pats relative performance.

As for the rest of the questions: incomplete analysis is incomplete. I don't really have a problem with the 5 yr window b/c aggregating it to that point gets you dozens of net fumbles, so you aren't totally pantsdown on a small variable quantity. I also don't see a problem having a question about that window!

Ideally all bloggers would show us details of their parameter selection... but... quickie bloggers gonna blog.

The linked analysis is terrible, but the WSJ did a writeup that took out most of the weaknesses and also noted that Patriots who had also played for other teams recently were much less likely to fumble in a Pats uniform. My quibble with the WSJ writeup is that it excludes dome teams (when it makes much more sense to exclude on gam conditions).

I will defend sports fans from MA generally, Red Sox fans especially, and most of all anyone who can help me get tickets to the August 31 Sox-Yankees game at Fenway for less than a hundred bucks a pop for bleacher seats.

No offense, Lemmy, but 86 is a pretty ridiculous bit of analysis. "Barry Bonds struck out twice in a game once" doesn't mean he wasn't a very, very good hitter. If the original analysis held value - and it may not! - the number of fumbles in one specific game is, literally, meaningless.

It wouldn't show conclusively, of course, but if (if!) the pats are a statistical outlier and not just by a little bit, and the other 31 teams aren't staffed by morons, we'd begin to suspect something. It would be interesting to investigate the psi-to-fumble-ability graph, by which I mean it would be interesting if someone else were to do it and report back. Where's the tipping point?

93: Right, but it's also plausible that other QBs have different preferences regarding optimal inflation, maybe preferring a higher chance of fumbles to the loss of airspeed or whatever. I'm assuming there's a tradeoff.

It could be. But the range of allowable PSI is pretty small (12.5-13.5) and the tested balls were short by 2 psi. God knows how low these monsters went on other occasions. The statistical stuff (arguendo!) suggests the patriots as outliers as a team and that there are changes in performance when players become/stop being patriots. First, it just seems more likely that the point of affecting performance in this measurable way is somewhere in that broad

How odd! the part that disappeared was completely convincing and said something like

...range below 12.5 rather than between 12.5-13.5. Second if the patriots are anomalous it suggests they're consistently doing something different, and no pressure in the narrow legal range is going to be unusual in games given natural variation and inaccuracy. It might be they aim for 12.5 exactly and just missed in a big way on this one occasion, but it seems less probable.

I just can't believe there's a league where you supply your own footballs but only for when you're attacking. It's asking for this to happen - surely the rule should just be that you play with the same pool of balls all the way through?

99: Yep. Since 2006. Here are articles from the NYT and WaPo from the season after they made the change that discuss it.

From the one:Carr, like several other quarterbacks, said Denver was one of the toughest places to play. He said he thought the ball expanded slightly at the altitude and felt slick because of the lower humidity. Before Houston's preseason game at Denver, Carr instructed the ball boys to let a little air out of the Texans' footballs.

I think the results of that preseason game should be reversed. (I forgot to mock ogged for the "forfeit" remark in the last post. )

The Commissioner has the sole authority to investigate and take appropriate disciplinary and/or corrective
measures if any club action, non-participant interference, or calamity occurs in an NFL game which he deems so
extraordinarily unfair or outside the accepted tactics encountered in professional football that such action has a major
effect on the result of the game.

111. So my position--you Khmer Rouge wannabe--is that wanting to characterize this as "so extraordinarily unfair or outside the accepted tactics encountered in professional football that such action has a major effect on the result of the game"--which has never (112) before been invoked in the history of the league reveals a critical flaw in the moral reasoning apparatus of the person or entity holding such a position.

Here's a discussion of the related "palpably unfair act*" (happens on the field) and other unfair situations in pro and college football.

*From the post: (Note: to my knowledge, there has never been a ruling of a palpably unfair act in the NFL. The NCAA rules are similar enough that college games are included below.)

Here is the data I saw (but only via a blog comment) on the fumble frequency of players who were on the PAtriots and other teams during the time period.

" Including recovered fumbles, Danny Amendola, BenJarvus Green-Ellis, Danny Woodhead, Wes Welker, Brandon LaFell and LeGarrette Blount have lost the ball eight times in 1,482 touches for the Patriots since 2010, or once every 185.3 times. For their other teams, they fumbled 22 times in 1,701 touches (once every 77.3)."

These are the kind of incidents which do lead to the rules being changed or adjusted* ** but asking for some kind of super penalty is the mark of the unthinking or the morally unserious.

*See some of the instances in the blog post referenced in 116.

*As the catch rule should be (or actually should have been done after the Calvin Johnson catch in 2010). The inclusion of more precision on "going to ground" or "act of catching the ball" would probably suffice. Until something exposed the cracks in that.

Kristol-lite, I think I speak for everyone when I congratulate someone of your advanced age for using the google to "support" your "point," but perhaps you could search "personal conduct policy" and not the narrower "palpably unfair act," and find the following:

All persons associated with the NFL are required to avoid "conduct detrimental to the integrity of and public confidence in the National Football League." This requirement applies to players, coaches, other team employees, owners, game officials and all others privileged to work in the National Football League.

In keeping with the penalties spelled out there, I'll settle for banishment of anyone involved in Ballghazi, and leave it up to the commissioner, in his wisdom, whether the game should be forfeit.

I was pretty sure this was a nothingburger drummed up to embarrass Belichick -- good job finding the only Patriots-cheating scandal I'm prepared to believe he knew nothing about, Colts; try teaching your guys how to behave during an onside kick* next time -- but that Kristol thing really is dispositive. I guess I can assume that not only did Belichick do it personally, he had a backup plan involving Curveball, yellowcake, and a ten-year occupation of Indianapolis. Hanging is too good for him.

* The thing about the "fumbles" vs. "fumbles lost" thing is that I absolutely believe that Belichick's players are better prepared to recover their own fumbles than the NFL at large; if Brandon Bostick had been a Patriot, he would have suffered some sort of Game of Thrones punishment, possibly involving being sewn inside a silk bag with angry bees, and would never be seen or even mentioned again.

I believe we already had this debate about exploiting the rules vs cheating in the context of that biting asshole who oppressed the Africans with his handball.
The problem with ogged's position, of course, it's its pretty much the maximum penalty for a small time technicality. Might as well go all "sweep the leg" on every opposing QB. Unless he does have higher levels of punishment planned under his Sharia regime, like beheadings.

|| Intimate encounter. Things are progressingsuccessfully. Your partner then apologizes and makes a quick trip to the bathroom. You remove your remaining clothing, expecting to soon proceed where things left off. Partner emerges from the bathroom, takes one look at you, and laughs.

I mean I thought it was some kind of weird hangover from back in the 1930s when footballs were in short supply and if the quarterback threw them all out or something the league would lose money or whatever. Not a 2004 "how can we make Brady's life easier" rule change.

More seriously, I'd just assume the laugh was of nerves or because they found you were a bit over-eager. Or because they remember the Friends episode where Joey takes off all his clothes when Monica went to get him some lemonade.

My understanding was that it was pretty widely a supported rule change by QB's across the league because they really do have varying preferences on that kind of thing. All the QB interviews I've seen confirmed that every QB in the league is doing minor things to the balls.

I guess it's no weirder than letting people use their own bat, but the idea of varying, personally customised balls just seems so weird to me. Isn't the ball meant to be a concrete expression of the absolute and universal values of western civilisation, an eternal verity which is uniform and consistent across all places and times?

Partner had already disrobed before heading to the toilet. I believe, in hindsight, the chuckle was a reflection of incompatible understandings regarding the completeness of the preceding course of events.

A life of celibacy sounds like a far less humiliating choice for the future.

154: The order of events is puzzling me. Traditionally, disrobing occurs near the beginning of lascivious activities and the end of said activities is indicated by getting dressed. It sounds like things happened in reverse.

It's hard on a face to be laughed in, as Charlie Brown said. Rule 34 implies CB saying something about hard-ons but I'm not looking.

saying something that appeals to their GGG while not whining is optimal, but what would work? Because of my childhood my queud-up lines were "kiss me, Hardy" & "Gentlemen, we have not yet begun to fight." The latter worked better.

151: American football really is an outlier in the sense of the QB having this unique constant tactile interaction with the ball. In soccer everyone is expected to be interacting with the ball and it's through a shoe so the feel isn't going to be a big deal. In baseball the pitcher handles the ball more than the rest of the team but not in the same lopsided manner as in football, and I think the individual feel of the ball means less in baseball because it's small and easy to grip.

Pitchers have been manipulating baseballs since baseball was invented, practically. Lots of cheating in baseball history with spit, shampoo or other liquid substances hidden in gloves or caps, intentional scuffing, etc. I don't know who's in charge of the supply of baseballs at games, though. Plus umpires inspect regularly these days.

Home team supplies the baseballs, all subject to inspection by the umpire. It is completely ridiculous that the NFL has 3 different sets of balls for a game -- kickers don't have preferences just like QBs?

The NCAA reverses results of games -- we won the Brawl in 2011 on just a retroactive ruling, having lost the game, and our pre-game no 1 national ranking, particularly ugly. Two Griz players were retroactively ruled ineligible for having received bail and free legal advice (for matters unrelated to football) from boosters.

169: Oh my, you got dressed? Here I'd been thinking along Moby's lines in 144, that the laugh/chuckle was over your eagerness, and at the time I'd probably have glanced at my naked self and chuckled too before making a beckoning gesture.

But this sounds very different. What the hell was wrong? Partner was already nekkid, correct? So your worst sin was ... thinking that you could be nekkid too? I must be missing something.

I may be misunderstanding, but it doesn't sound as if you were the asshole there. I don't quite get it, but it sounds as if your partner perceived whatever the two of you were doing as a completed sexual encounter, and then laughed at you for thinking there was more to come? That sounds as if they were being a jerk. (Is partner's gender available information?)

This seems intrusive, but that's what we do here -- did your partner get off? This seems like a totally different situation if they got theirs, went to the bathroom, and then came out, laughed at you, and left you hanging, or, on the other hand, if the two of you did whatever messing around you did, and your partner decided mid-event that they didn't want things to progress any further.

I mean, in either case, bad communication and it sounds like it's from them not you, but in the first case they're a real jerk, and in the latter case maybe just awkward a bit.

182: If you don't know the person well, that sounds right, but based on what you've said I wouldn't feel bad about it at all.

If you know them reasonably well, and they're generally not an asshole, it's probably worth a "So, what happened last night? Suddenly, after you went to the bathroom, everything was awkward." I mean, possibly you need someone to mention that it was a turnoff when you asked if they'd wear a pickelhaube for you. Or something.

The sexual encounter seems to have existed in some radically indeterminate state between clothed and not clothed, sex and not sex, bathroom and not bathroom, orgasm and not orgasm. initiation and completion. Maybe the laughter was actually just joy at watching the ordinary laws of classical mechanics collapse around you.

186: DB: I certainly don't think you are under any obligation to contact this person again if you don't know them all that well, but I think it might be worth a check-in in any case, just to see if they are willing to talk with you about what happened. Worst case, you confirm that they are, in fact, a jerk. Better case: you both get to talk about how your expectations got off track, and can put this information to use in future encounters with other people. Best case: after some possibly embarrassing mutual revelations, you both decide that you'd like to try again in some way with better communication up front, and have a much better experience the second time around.

Or maybe this is a time-reversal / causality problem? Schrodinger's problem was different:

His position at Oxford did not work out well; his unconventional domestic arrangements, sharing living quarters with two women[8] was not met with acceptance. In 1934, Schrödinger lectured at Princeton University; he was offered a permanent position there, but did not accept it. Again, his wish to set up house with his wife and his mistress may have created a problem.

Yikes, DB, yes, laughing was cruel, and even though I can imagine myself doing something like that (nervous laughter), I would have mustered an apology right away. Goodness knows it's terribly stressful to disrobe in front of someone new.

218: I dated a poorly endowed fellow once upon a time. He was so terribly insecure about it that I'd never have forgiven myself for laughing. I feel like it's the sort of thing one should know, or at least suspect, in advance.

I was going to make the point in 225, and then thought that if we're looking for precision here, it's not impossible that DB is a trans woman, which would allow for the possibility of non-straight sex involving one person with balls and one person with a pussy, so knecht wasn't necessarily being heterosexist. But I would guess that teo's right and knecht was assuming straight sex.

Because if there's anything that's important in the broad genre of cock jokes, it's precision.

There's a separate question I've thought about in terms of people who say "I'm about to come" when they are, because I don't have a wide enough sample size to generalize (laydeez!) but have generally thought it makes sense during fellatio if it's not clear what the response will be and makes sense for people who are generally chatty about/during sex and presumably for other reasons too. But is it a social norm I'm just missing for whatever personal reasons?

But is it a social norm I'm just missing for whatever personal reasons?

I wouldn't say it's a social norm, but if you want your partner not to stop doing what they're doing, or if you want to let them know to come with you, and probably some other reasons I'm not thinking of, it makes sense.

234: I'd thought of the first after posting, but the second wouldn't have been as obvious to me even though in retrospect I know it can work that way. (And I mostly thought of this because it happened in a movie Lee was watching last night and I think was supposed to signal that the people having sex, although married, we're sort of strangers to each other. But maybe I was overreading)

My FB feed is full of Pats fans being hyper-defensive about how UNFAIR and STUPID the whole thing is. And I just can't stop thinking: if the Seahawks stood accused of breaking a rule, you'd be having a field day about it on this same social-media platform. So maybe calm the fuck down, and let the investigation happen.

In an autopsy report of 5559 instances of sudden death, 34 (0.6%) reportedly occurred during sexual intercourse. Two other autopsy studies reported similarly low rates (0.6%-1.7%) of sudden death related to sexual activity. Of the subjects who died during coitus, 82% to 93% were men, and the majority (75%) were having extramarital sexual activity, in most cases with a younger partner in an unfamiliar setting and/or after excessive food and alcohol consumption. The increase in absolute risk of sudden death associated with 1 hour of additional sexual activity per week is estimated to be

Nelson Rockefeller's body was cremated only 18 hours after he was pronounced dead, because Happy Rockefeller, his proper wife, did not want the Medical Examiner's Office to examine his body for evidence for sexual ejaculation.